hw3 - MATH 138: Calculus 2 Assignment #3 Due: 12:30 p.m.,...

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Unformatted text preview: MATH 138: Calculus 2 Assignment #3 Due: 12:30 p.m., Friday, October 8 Fall 2010 1. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region and the solid. (a) y = 1 − x2 , y = 0; about the x-axis. √ (b) x = 2 y , x = 0, y = 9; about the y -axis. 1 (c) y = x2 , y = 5 − x2 ; about the x-axis. 4 1 (d) y = x2 , x = 2, y = 0; about the y -axis. 4 2. Determine whether each integral is convergent or divergent. Evaluate those that are convergent. ∞ (a) 1 0 1 dx. (3x + 1)2 1 dx. 2x − 5 xe−x dx. 2 (b) −∞ ∞ (c) −∞ ∞ (d) 2π 3 sin θdθ. √ 1 dx. 3−x (e) 2 3. Use the Comparison Test to determine whether the integral is convergent or divergent. ∞ (a) 1 ∞ (b) 1 ∞ (c) 1 x dx. +1 2 + e−x dx. x x dx. 2+1 x x3 The following problems are only recommended, not for submission. • Course Notes: Do all examples in Sections 1.2 and 1.4. • Stewart: Section 6.2 Exercises 9, 11, 54; Section 7.8 Exercises 43, 57, 58; Do all examples in Sections 6.2 and 7.8. ...
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